Area potential function (\(U_t^a\) )   The area potential \(U_t^a(f)\)  at a frontier \(f\)  measures the amount of free-space left to explore beyond \(f\) , i.e., navigable cells which are unexplored in the partial semantic map. To calculate \(U_t^a(f)\)  on training data, we first group the unexplored free-space cells into connected components \(C = \lbrace c_1, \cdots , c_n\rbrace \)  using OpenCV [1]}, and then associate each connected component \(c_i\)  to the map frontiers. A component \(c\)  is associated with frontier \(f\)  only if at least one pixel in \(c\)  is an 8-connected neighbor of some pixel in \(f\) . For each frontier \(f\) , we can then calculate the area potential \(U_t^a(f)\)  as the sum of areas of connected components associated with \(f\) , normalized by the total free-space on the complete map. To get the overall area potential function \(U_t^a\)  for the map, we set all non-frontier pixels to 0, and set a frontier's area potential to the corresponding frontier pixels (as shown in Fig. REF , column 3).
